Based on the COBE results combined with smaller-scale constraints
from galaxies, galaxy clusters, and large-scale structure, it has
become apparent that there are several ways to modify the
CDM model to reduce its excessive small-scale power
(Efstathiou et al 1992,
Wright et al 1992).
These include "tilting" the primordial
power spectrum index to n < 1 (TCDM), replacing some of the
CDM with HDM that clusters much less efficiently
on small scales (HCDM), replacing some of the CDM with a cosmological
constant
that does not
cluster at all (LCDM),
and simply eliminating most of the matter, leaving an open universe (OCDM).
All these models retain the assumption of "adiabatic" primeval
perturbations of the sort produced during inflation
(Guth & Pi 1985).
Dodelson et al (1996)
have recently reviewed the status of the expanded family of CDM models.

The most obvious way to reduce small-scale power, while retaining
consistency with the large-scale power required for microwave background
anisotropy, is to decrease the primeval spectral index n of
Equation 10, which is a possibility allowed by inflationary models.
The TCDM model has been investigated with simulations by
Cen et al (1992),
Cen & Ostriker
(1993a),
Gelb et al (1993),
Moscardini et al
(1995).
Based on their results and the more recent summaries by
White et al (1995),
Cole et al (1997),
it appears that TCDM models with 0.7
n 0.9 remain viable,
although they are less attractive than some of the other alternatives.

The HCDM model is attractive because the extra ingredient added to the
CDM model is a particle that is known to exist and whose abundance is
predicted in standard cosmology, the neutrino. The twist is that one or
more flavors of neutrino must have nonzero masses adding up to
18.7 h2( / 0.2)
eV, where is the fraction of the
critical
mass density in massive neutrinos. The first simulations of this model,
performed by
Davis et al (1992b),
Jing et al (1993),
Klypin et al (1993),
showed that with
= 0.3, the HCDM model
is in better agreement with observations of pairwise velocities and
large-scale structure than the CDM model.
Bryan et al (1994)
showed that this model also
succeeds in reproducing the observed abundance of X-ray clusters.
However, simulations by
Cen & Ostriker
(1994b),
Ma & Bertschinger
(1994b),
Klypin et al (1995)
showed that galaxy formation occurs too late unless
is decreased in order to
increase the small-scale power. HCDM with
= 0.2 (with one or two
massive neutrino flavors) remains an attractive model, although it may
overproduce rich clusters
(Cen & Ostriker
1994b,
Borgani et al 1997).
Liddle et al (1996b)
gave a recent review.